Extended affine Weyl groups

DOI10.1006/jabr.1998.7693zbMath0927.17013OpenAlexW1985622244MaRDI QIDQ1291082

Saeid Azam

Publication date: 15 December 1999

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jabr.1998.7693

zbMATH Keywords

presentationWeyl groupHeisenberg groupsemidirect productaffine Lie algebraaffine root system

Mathematics Subject Classification ID

Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras (17B67) Reflection and Coxeter groups (group-theoretic aspects) (20F55) Simple, semisimple, reductive (super)algebras (17B20)

Related Items (20)

The Structure of a Presented Group Associated to an Extended Affine Root System ⋮ A Length Function for Weyl Groups of Extended Affine Root Systems of Type A₁ ⋮ Characterization and enumeration of reflectable bases of types E6,7,8 ⋮ Integrable representations for the twisted full toroidal Lie algebras ⋮ Unnamed Item ⋮ Nonreduced extended affine Weyl groups. ⋮ Reflectable bases for affine reflection systems ⋮ Combinatorics of extended affine root systems (type A1) ⋮ On the presentations of extended affine Weyl groups. ⋮ On the relation of extended affine Weyl groups and indefinite Weyl groups. ⋮ Simply laced extended affine Weyl groups (a finite presentation). ⋮ The Abelianizations of Weyl groups of root systems extended by Abelian groups ⋮ Classification of irreducible integrable representations for the full toroidal Lie algebras ⋮ A graph-theoretical classification for reflectable bases ⋮ Extended Affine Weyl Groups: Presentation by Conjugation via Integral Collection ⋮ Extended affine Weyl groups of type \(A_1\). ⋮ Presentation by conjugation for \(A_1\)-type extended affine Weyl groups. ⋮ Presentation by conjugation for \(A_1\)-type extended affine Weyl groups. ⋮ Integral structures in extended affine Lie algebras ⋮ Groups of extended affine Lie type

Cites Work

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• Extended affine root systems. II: Flat invariants
• Toroidal Lie algebras and vertex representations
• Extended affine root systems. I: Coxeter transformations
• Vertex representations for \(n\)-toroidal Lie algebras and a generalization of the Virasoro algebra
• Enveloping algebras and representations of toroidal Lie algebras
• Extended affine root systems. III: Elliptic Weyl groups
• Classification and construction of quasisimple Lie algebras
• Quantum tori and the structure of elliptic quasi-simple Lie algebras
• Lectures on Chevalley Groups
• Observations on group rings
• Extended affine Lie algebras and their root systems
• Nonreduced extended affine root systems of nullity 3
• The Alternative Torus and the Structure of Elliptic Quasi-Simple Lie Algebras of Type A 2
• Introduction to Lie Algebras and Representation Theory

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